Error with serial connection of springs

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Error with serial connection of springs

Postby glitchrain » Sun May 31, 2015 9:58 am

Hi!

I think I found an error with serial connection of springs. Everything alright with parallel connection of springs. But serial one include error.

I conducted little experiment. I used four identical circles, three identical springs and connected its with two different ways. I connected first couple of circles by means of sequence of two springs. Second one was connected by means of one spring, but one of circles was fixed in space.

Image

And these was two oscillators. Their angular frequency can be calculated by using formula w=sqrt(k/m) where k=coefficient of stiffness(reduced in first case and ordinary in second), m = mass(also reduced in first case and ordinary in second).

For the second oscillator:
Angular frequency is w=sqrt(k/m).

For the first oscillator:
1/K=1/k+1/k
Reduced coeff. of stiffness is K=k/2, where k - stiffness of one spring.
Reduced mass is M=m/2.
And angular frequency is w=sqrt((k/2)/(m/2))=sqrt(k/m).

Image

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They must have identical angular frequency. But they don't. As you can see on appendix difference is near 1.5 time. I think it is sqrt(2). And that mistake can appear when coefficient of stiffness doesn't change.

P.S. I apologize for my bad english.*^^*
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Re: Error with serial connection of springs

Postby pnvv » Wed Jun 03, 2015 2:55 pm

Your english is fine. I couldn't understand it cause I'm crap at math! ;)
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(/)(°,,,°)(/)
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Re: Error with serial connection of springs

Postby jon_joy_1999 » Mon Jun 15, 2015 2:10 am

glitchrain wrote:Hi!

I think I found an error with serial connection of springs. Everything alright with parallel connection of springs. But serial one include error.

I conducted little experiment. I used four identical circles, three identical springs and connected its with two different ways. I connected first couple of circles by means of sequence of two springs. Second one was connected by means of one spring, but one of circles was fixed in space.
No. The first pair of springs are not connected together in any meaningful way. They are actually (as evidenced by the anchor colors in your screenshots) connected to the background. You've essentially got the same thing on the left as you do on the right, and my psychic powers suggest that you've altered the force of the spring on the right without the corresponding alteration in mass of the circle on the right.
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